There will be a second round of voting later this week and, if approved, a referendum will follow.
Critics claim it amounts to a power grab by Mr Erdogan.
But the president says the changed system will resemble those in France and the United States.
The new constitution will allow the president to appoint and dismiss ministers, and it will abolish the post of prime minister for the first time in Turkey's history.
Instead there will be at least one vice-president.